_ k=0 ^ 20 ( ^ 20 C_ k )^ 2 is equal to : - Vidyadip

MCQ

$\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}$ is equal to :

A
${ }^{40} \mathrm{C}_{21}$
B
${ }^{40} \mathrm{C}_{19}$
✓
${ }^{40} \mathrm{C}_{20}$
D
${ }^{41} \mathrm{C}_{20}$

✓

Answer

Correct option: C.

${ }^{40} \mathrm{C}_{20}$

c
$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$

sum of suffix is const. so summation will be ${ }^{40} \mathrm{C}_{20}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Given sum of the first $n$ terms of an $A.P.$ is $2n + 3n^2.$ Another $A.P.$ is formed with the same first term and double of the common difference, the sum of $n$ terms of the new $A.P.$ is

A person $X$ is running around a circular track completing one round every $40 s$. Another person $Y$ running in the opposite direction meets $X$ every $15 s$. The time, expressed in seconds, taken by $Y$ to complete one round is

The sum of all two digit numbers which, when divided by $4$, yield unity as a remainder is

$\mathop {\lim }\limits_{x \to \pi /4} \frac{{{{\cot }^3}\,x - \tan \,x}}{{\cos \left( {x + \pi /4} \right)}}$ is

Square matrix ${[{a_{ij}}]_{n \times n}}$ will be an upper triangular matrix, if

If $\left| {\,\begin{array}{*{20}{c}}a&b&{a + b}\\b&c&{b + c}\\{a + b}&{b + c}&0\end{array}\,} \right| = 0$; then $a,b,c$ are in

Which of the following statements is incorrect for a square matrix $A. ( | A | \neq 0)$

If$\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, where $0 < \theta < {180^o}$, then $\theta =$

If $f$ and $g$ are continuous functions on $[0,\,\,a]$ satisfying $f(x) = f(a - x)$ and $g(x) + g(a - x) = 2,$ then $\int_0^a {f(x)g(x)\,dx = } $

Which of the following sequence is an arithmetic sequence